29Ans 1 \int_{0}^{100}{[tan^{-1}x]} = \int_{0}^{tan1}{0dx} + \int_{tan1}^{100}{dx} = 100 - tan1
Ans 3\int_{1}^{\sqrt{2}}({x+1})dx + \int_{\sqrt{2}}^{\sqrt{3}}({x^{2}+4})dx + \int_{\sqrt{3}}^{2}({x^{3} +9})dx
plz post the solutions for these questions
1) find the value of \int_{0}^{100}{[tan^{-1}x]} where [] equals gretest integer function
2)find the value of \int_{-2}^{2}{min {x-[x],-x-[-x]}dx } where [] denotes greatest integer function
3)\int_{1}^{2}{(x^{[x^{2}]}+[x^{2}]^{2})dx}
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2 Answers
2929Ans 2 ..use the property that [-x] = -(1+[x]) and x -[x] = {x}
so u will get the function as
f(x) = min( {x} , 1 - {x} )
now u wll get four triangles on the x axis with base 1 unit and height 0.5 unit ..so total area = 1 unit2
